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采用AFM和Raman連用係統表征單壁碳納米管
日期：2024-04-20 05:05
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摘要：
In situ Raman Measurements of
Suspended Individual Single-Walled
Carbon Nanotubes under Strain
Sang Wook Lee,† Goo-Hwan Jeong,† and Eleanor E. B. Campbell*,#
Department of Physics, Go¨teborg UniVersity, Go¨teborg, SE-412 96,Sweden
Received April 14, 2007; Revised Manuscript Received July 19,2007
ABSTRACT
We present a technique for in situ Raman measurements of suspendedindividual single-walled carbon nanotubes (SWNTs) under strain.We
observe a strong change in the radial breathing mode intensity withincreasing strain as the nanotube moves out of (or into) resonance,and
for strain greater than 2%, there is a clear irreversible upshiftin the G-mode frequencies accompanied by an increase in intensityof a broad
peak at a position associated with the D mode. For lower strain,the G-mode peaks (A1, E1, and E2) do not change significantly inposition but
change in relative intensity.
Due to their remarkable mechanical and electrical properties,
carbon nanotubes (CNT) continue to be the object of intense
experimental and theoretical investigation. Applications of
the CNT’s mechanical properties within lightweight composite
materials1 are now reaching commercial products, and
efforts are proceeding to increase the Young’s modulus of
nanotube yarns and mats to approach the theoretical limit.2
The mechanical and electrical properties of individual carbon
nanotubes have also been the object of much fundamental
interest. In recent years, CNT-based nanoelectromechanical
systems3-10 have been studied to investigate the interesting
coupling of electrical and mechanical behavior that occurs
on the nanoscale. The change of the electronic properties of
an individual CNT as mechanical force is applied is one of
the most intriguing issues within this larger topic.4-7
Structural and electronic properties of single-walled carbon
nanotubes (SWNTs) under strain have been theoretically
investigated by employing different calculation methods.11-13
Most of these theoretical studies deal with the changes of
bond lengths, radii, and band gaps of specific SWNTs as a
function of compressive and tensile strain. It is clear from
these results that the band gap of the SWNTs can change
significantly as strain is applied. This was confirmed in an
experimental study of transport measurements on individual
suspended SWNTs under strain.4 Concerning structural
changes, Pullen et al.13 recently used an ab initio approach
to show that there was a small, chirality-dependent, linear
increase in bond length with strain, except for bonds directed
along the nanotube circumference. They also predicted that
the radii remain unchanged under uniaxial strain up to 6%.
Resonant Raman spectroscopy is a powerful tool to probe
structural and electronic changes of SWNTs in experiment.14
There have been several experimental studies devoted to the
investigation of changes in the Raman spectra when applying
pressure or strain on bundles of SWNTs.15-19 The tangential
and radial breathing modes (RBM) of SWNT bundles were
shown to shift both under compressive15,16 and tensile17-19
force. In the case of SWNT bundles, there is the added
complication of the tube-tube interaction and how it affects
the Raman spectra under external forces. Cronin et al.20,21
reported Raman studies of individual SWNTs deposited on
a silicon substrate that were placed under strain bymanipulating
the nanotubes with an AFM tip (pushing the central
part of the nanotube across the substrate) and studying the
Raman spectra before and after manipulation. They observed
a very clear downshift in the position of the G band which
was much larger than that observed by the same group in
later experiments on bundles of nanotubes where the strain
was applied via an elastic polymer substrate.19 In all of the
studies reported so far, there have been interactions either
between individual nanotubes or between a nanotube and a
substrate, which can serve to complicate the effects. In the
present work, we apply strain to individual suspended
SWNTs grown between a Si cantilever and a support. The
strain is applied by deflecting the cantilever with an AFM
tip while simultaneously recording the Raman spectra. The
results are qualitatively different from those reported by
Cronin et al.20,21
The experiments were carried out using a combined
Renishaw/Nanonics micro-Raman/AFM setup. The AFM tip
* To whom correspondence should be addressed. E-mail:
Eleanor.Campbell@ed.ac.uk.
† Equal contribution to this work.
# Also at School of Chemistry, Edinburgh University, West MainsRoad,
Edinburgh EH9 3JJ, Scotland.
NANO
LETTERS
2007
Vol. 7, No. 9
2590-2595
10.1021/nl070877x CCC: $37.00 © 2007 American Chemical Society
Published on Web 08/25/2007
was used to deflect a Si cantilever which formed one support
of a suspended SWNT, shown in Figure 1. Axial strain was
applied to the nanotube by deflecting the cantilever via a
force applied by the AFM tip. As was the case for the studies
of nanotubes deposited on substrates, the deflection force
was applied perpendicular to the nanotube axis; however,
the resulting strain was primarily uniaxial.21 In the present
experiments, we could also rule out any contribution from
torsional strain, which was less straightforward for theearlier
studies. The micromechanical silicon cantilever structures
were fabricated by selective plasma etching of Si and wet
etching of SiO2 with buffered hydrofluoric acid. The dimensions
of the cantilever (70 ím long, 4 ím thick, 4 ím wide)
and the counterpart support platform were defined by electron
beam lithography on a silicon-on-insulator (SOI) wafer. The
distance between the cantilever and the platform was
typically 1-2 ím.
SWNTs were synthesized by thermal chemical vapor
deposition. As-purchased ferritin solution (Sigma Aldrich)
was diluted (0.01 vol %) with deionized water and deposited
on the cantilever to serve as the catalyst for SWNT growth.22
After calcination of the ferritin molecules, SWNTs were
grown using methane and hydrogen gas at 900 °C for 5 min.
The ferritin density was adjusted to ensure that, on average,
one suspended SWNT was grown between the cantilever and
the platform. Strain-force-dependent resonant Ramanspectroscopy
was performed on the individual suspended SWNTs
by combining an AFM head (Nanonics Imaging Ltd.) with
a micro-Raman measurement system (Renishaw) operated
with a 514.5 nm laser. The AFM tip was placed at the center
of the silicon cantilever. The cantilever was long enough to
avoid the screening of the laser beam by the AFM tip since
the average width of the commercially available AFM probe
is around 30 ím. The spring constant of the silicon cantilever
was estimated at the center by force-distance measurements
with an AFM tip (spring constant of the AFM cantilever
was 15 N/m) and found to be 18 N/m. From the force
calibration, shown in Figure 2, we could determine a linear
relationship between the deflection voltage of the AFM
system and the height difference at the center of the
cantilever. A deflection voltage of, for example, 0.5 V
induces a 22.5 nm height difference, corresponding to a
downward deflection of 45 nm at the end of the cantilever.
Resonant Raman spectroscopy measurements were done
while the AFM tip was pushing on the silicon cantilever.
Each time the force was increased on the cantilever, the laser
that monitored the deflection of the AFM tip was screened
by a homemade shutter to aid focusing and also to prevent
any interference with the Raman signal from the stretched
SWNT. It was also possible to check the position of the end
of the AFM tip when the shutter was in place, as shown in
the left-side inset of Figure 2. The focus of the micro-Raman
laser spot was adjusted to coincide with the suspended
SWNT after the spot was located exactly in the gap space
between the end of the silicon cantilever and the platform.
The focus was readjusted each time after increasing the
pushing force on the cantilever. As has been noted previously,
23 the Raman signal from suspended SWNTs is much
stronger than the signal from SWNTs lying on the substrate,
which, combined with the poor focus conditions in our
experiment for the nanotubes on the substrate, means that
we only detect the Raman signal from the suspended
nanotube.
Figure 3a shows the strain-force dependence of the
resonant Raman spectra of a suspended SWNT. The maximum
strain used in this series of measurements was estimated
to be 1%. There is some uncertainty in this value due to
the uncertainty in the amount of slack present initially in
the suspended nanotube and the possible influence of
slippage at the high deflections. The strain values used
throughout this paper are estimated assuming an initially taut
nanotube and no slippage. We have carried out systematic
measurements to estimate the effect of slippage. We did not
observe any indication of slippage for nominal applied strain
of up to 1%. We have also not observed any abrupt changes
in the Raman spectrum for these relatively low strain values
that can be attributed to slippage, as was observed by Kumar
and Cronin for nanotube bundles.19 Beyond this nominal
strain value, we observed irreversible changes in the Raman
spectra due to damage of the nanotubes. It is probable that
a certain degree of slippage was occurring for these extreme
strain values, but at present, this is difficult to quantify.
The frequencies and fwhm of the measured Raman peaks
were determined by fitting the spectra assuming Lorentzian
line shapes. The error bar on the experimental frequency and
Figure 1. (a) Typical SEM image of silicon cantileverstructure.
Scale bar shows 10 ím. Inset: zoomed-in SEM image of individual
SWNTs suspended between the end of the cantilever and the
platform. (b) Schematic configuration of the setup for astrain-forcedependent
in situ resonant Raman measurement. L0 is the length
of the suspended SWNT, and 2ä is the downward distance of the
SWNT due to deflection of the silicon cantilever by AFM tip
manipulation.
Nano Lett., Vol. 7, No. 9, 2007 2591
fwhm is typically on the order of 1 cm-1. The radial breathing
mode is clearly seen at 169 cm-1. According to the
relationship given by Meyer et al.,24 determined forfreestanding
SWNTs, this corresponds to a semiconducting
nanotube with a diameter of 1.45 nm and is most probably
an (11,10) nanotube. Examples of some fitted tangential (Gband)
modes for the same nanotube are shown in Figure 3b.
The Raman laser was not aligned parallel to the nanotube
axis so all six allowed transitions could be observed,
corresponding to transitions with A, E1, and E2 symmetry
for both the G+ and G- bands. The peak positions and fwhm,
determined without strain applied to the nanotube, are listed
in Table 1 (SWNT1). There is an upshift/downshift (öG-
/öG+) in the measured frequencies compared to the values
reported for nanotubes of the same diameter isolated on a
Si/SiO2 substrate25 by 3-5 cm-1 for the A and E1 transitions
and by +12 cm-1 (öG-) and -16 cm-1 (öG+) for the E2
transitions. A similar trend is noted for the second nanotube
(öRBM ) 186 cm-1, d ) 1.28 nm, most probably (10,9)),
whose values are given in Table 1 (SWNT2, spectra provided
as Supporting Information). All six Lorentzians are needed
to obtain a good fit to the data, although the E2 transitions
are typically lower in intensity than the A and E1 transitions.
The fitted line widths are consistent with the natural line
widths of the transitions.26 In addition to the sharp peaks, it
is also necessary (in particular for high strain) to fit broad
features at 1540 (fwhm ca. 100 cm-1) and 1610 cm-1
(fwhm ca. 60 cm-1). These features have been noted
previously in weakly resonant G-band spectra fromsemiconducting
SWNTs and associated with a double-resonance
process.14,25,27 We observe that the broad features are more
intense in spectra with small radial breathing modeintensities,
that is, for tubes that are only weakly resonant, in
agreement with previous observations.
Some clear tendencies can be observed in the straindependent
measurements. The radial breathing mode frequency
does not shift with increasing strain within our
experimental uncertainty. This is in agreement with recent
calculations13 and with the experimental study of individual
strained nanotubes on a substrate by Cronin et al.20 However,
in contrast to the study of Cronin et al., we do observe a
clear change in the intensity of the radial breathing mode
transition. This is shown in more detail in Figure 4 where
the integrated RBM peak intensities are plotted as a function
of the AFM deflection voltage (and estimated strain). Two
sets of data are shown here. Figure 4a corresponds to the
spectra shown in Figure 3 and Figure 4b to the results from
SWNT2. The strain applied to the nanotube can be estimated
according to the approximate relation strain [%] ) B voltage2, withB ) 0.1 for SWNT1 (length ) 2 ím) and B
) 0.4 for SWNT2 (length ) 1 ím). For SWNT1, which
initially showed an intense RBM signal, the intensity falls
off linearly with increasing strain until it disappearscompletely
for AFM deflection voltages greater than 2.5 V
(estimated strain > 0.6%). For SWNT2, which initially
showed a very weak RBM peak (indicating only weak
resonance), the RBM intensity first increases as strain is
applied, reaching a maximum for a strain of approximately
0.4%, and then decreases toward zero. This can be explained
in terms of the deformation of the electronic band structure
with the application of strain.13,17 The experimental resonance
window for the RBM of isolated, suspended nanotubes is
on the order of 8 meV.28 Band gap changes significantly
larger than this can be expected for the strains applied in
the present experiments.4,13 The overall intensity of the G
band does not change so dramatically (the resonance window
is much less critical for the G peaks since the phonon energy
is larger28), but a close look at the spectra in Figure 3 shows
Figure 2. Force-deflection curve of a silicon cantilever. Thepushing force is applied in the middle of the cantilever using AFMtip
manipulation. Upper inset: optical microscope image of the devicewhen the AFM tip pushed the cantilever (upper) before and(lower)
after the shutter screened the laser from the AFM head. Lowerinset: force-displacement curve measured on the cantilever (redline) and
on a Si substrate (black line) for calibration of the springconstant of the cantilever.
2592 Nano Lett., Vol. 7, No. 9, 2007
that the relative intensities of the A and E1 peaks of the G+
band undergo strong changes as strain is applied. This
behavior has been found to be strongly dependent on the
individual nanotube, with some nanotubes showing relatively
little change in relative intensities for a similar nominalstrain
range. However, the changes in the relative intensities for a
given individual nanotube are reproducible and reversible.
Figure 5 shows that the G+ A/E1 ratio for SWNT1 reaches
a minimum for AFM deflection voltages in the range of 0.4-
1.5 V (ca. 0.16-0.22% strain) before rapidly increasing again
to a maximum at 2.5 V (0.6% strain). Interestingly, the
minimum in the G+ A/E1 ratio is accompanied by the
appearance of a small, narrow peak at the position of the D
mode (1333 cm-1, fwhm 5 cm-1). Such behavior is not
observed for every nanotube, and we assume that it is related
to a resonant process with a relatively narrow resonance
window. Detailed ab initio calculations are required to
elucidate the mechanisms for these changes, but it is clear
from these spectra that strain measurements on suspended
nanotubes have the potential to provide a very stringent test
of theoretical studies of the electronic structure andtransition
matrix elements of individual nanotubes.
The G-band peak positions are plotted in Figure 6 as a
function of the applied strain for SWNT1 (Figure 5a) and
SWNT2 (Figure 5b). In contrast to the study of Cronin et
al. for nanotubes deposited on a substrate,20,21 we do not
observe any down-shift in the frequencies of the G-band
transitions. For both nanotubes, we observe an increase in
the frequencies as the strain is increased beyond a certain
critical value (ca. 2% in both cases). This effect is more
apparent for SWNT2 (Figure 5b), which is exposed to higher
strain and where it is also possible to see that the frequency
shift is larger for the G- peaks than that for the G+ peaks.
Figure 3. Deflection-force-dependent in situ resonance Raman
spectroscopy result on a suspended individual SWNT. (a) Change
of Raman spectra depending on AFM deflection voltage (lower
x-axis) and estimated strain (upper x-axis) from 0.0 to 3.0 V.(b)
G-band peak fits for three different values of the estimatedstrain.
Table 1. Fitted Lorentzian Peak Positions and fwhm for TwoSuspended SWNTs without the Application of Strain; the DiameterHas
Been Calculated Using the Expression Given by Meyer et al.,24 öRBM[cm-1] ) 204/d [nm] + 27
RBM diam. G-A G- E1 G- E2 G+A G+ E1 G+ E2
SWNT1, ö 169 1.45 nm 1572 1576 1566 1590 1586 1594
SWNT1, fwhm 5 5 4 5 6 5.3 6
SWNT2, ö 186 1.28 nm 1568 1575 1563 1590.5 1586 1595
SWNT2, fwhm 7 7 7 7 6 5.3 6
Figure 4. Integrated radial breathing mode (RBM) intensity as a
function of AFM deflection voltage (lower x axis) and estimated
strain (upper x axis) for (a) SWNT1 and (b) SWNT2.
Nano Lett., Vol. 7, No. 9, 2007 2593
For an applied AFM deflection voltage of 5 V or higher on
SWNT2 (g10% strain), it was not possible to resolve the
individual peaks and, only two Lorentzians were used to fit
the data instead of six. Once we observed this shift in the
G-peak frequencies, the spectral changes were no longer
reversible. We therefore attribute the change in thefrequencies
to the occurrence of damage in the nanotubes.
In addition to the small, sharp D peak visible in the spectra
shown in Figure 3a, there is a much broader peak centered
at 1367 cm-1 (independent of applied strain) with a fwhm
of 200 cm-1. This becomes clearly visible for large strain
and is observed in both sets of spectra (SWNT1 and
SWNT2). The integrated peak intensities for both nanotubes
are plotted in Figure 6c as a function of AFM deflection
voltage. We often observe a small, finite, broad peak intensity
for zero force applied to the silicon cantilever, which then
disappears for low values of strain (up to ca. 1%) before
increasing strongly as the strain is increased beyond this
value. Such behavior can be clearly seen in Figure 6c for
both samples. The finite peak intensity for zero force may
be related to initial slack in the suspended nanotube, although
this is too small to be observed by SEM. Alternatively, it is
conceivable that the application of a small strain can help
heal some intrinsic defects in the nanotube.
In summary, we have measured in situ Raman spectroscopy
of suspended individual SWNTs under strain. The
position of the radial breathing mode frequency remains
constant as strain is increased, but the intensity changes due
to the modification of the band structure, leading to a change
in the resonance conditions. This observation is in agreement
with calculations for semiconducting nanotubes.13,17,21 The
results concerning the G-mode peaks are more unexpected.
One would intuitively expect that an increase in nanotube
length would lead to a corresponding increase in the bond
length in the axial direction and hence to an expected
decrease in frequency. A large down-shift was also observed
in earlier experimental work.20,21 However, in the present
experiments, the positions of the G-mode peaks do not
change significantly until the strain exceeds 2%, when one
can observe an upshift in the frequency. These changes to
the spectra are irreversible and indicate that structuralchanges
have occurred. The effect is most pronounced for the Gpeaks.
Below this, although the peak positions remain
constant, there can be strong variations in the relative peak
intensities both for the G mode and the D mode. These
changes are reversible and are attributed to changes in the
band structure affecting the resonance conditions. Both
Figure 5. (a) Ratio of integrated A/E1 peak intensities(triangles
and left-hand y axis) and (b) the integrated sharp (1333 cm-1,fwhm
5 cm-1) D-peak intensity (stars, right-hand axis) as a functionof
AFM deflection voltage (lower x axis) and estimated strain(upper
x axis). The integrated peak intensities were normalized to theSi
peak intensity for each spectrum.
Figure 6. (a) G-mode peak positions as a function of AFM
deflection voltage (lower x axis) and strain (upper x axis) for
SWNT1. (b) G-mode peak positions as a function of AFM
deflection voltage (lower x axis) and strain (upper x axis) for
SWNT2. The large error bars for 5 and 5.5 V indicate that the
individual peaks could not be clearly resolved, and both the G+
and G- bands were each fitted with a single Lorentzian. Thedotted
lines mark the initial position of the peak for zero appliedstrain
and are simply to aid the eye. (c) Integrated broad D-modeintensity
(1367 cm-1, fwhm 200 cm-1) as a function of estimated strainfor
SWNT1 (squares) and SWNT2 (stars).
2594 Nano Lett., Vol. 7, No. 9, 2007
nanotubes that we studied in detail in the present paper are
very close to the armchair in geometries (11,10) and (10,9).
We would therefore not expect a significant shift in the
frequencies of the transverse G- peaks, in agreement with
our experimental observations, since the relevant bond
lengths would not be significantly effected by the appliance
of axial strain. However, we would still expect thelongitudinal
G+ peaks to shift downward. Reich et al.29 carried out
full ab initio calculations on two chiral nanotubes and showed
that chiral tubes yield qualitatively and quantitativelydifferent
results from achiral ones, with evidence for a strong
mixing of the optical modes. The situation is therefore
considerably more complex than might be assumed from
tight-binding calculations, and we hope that our present
results might stimulate more theoretical studies into the
properties of chiral nanotubes.
In addition to the sharp Lorentzian peaks that have a fwhm
close to the natural line width, there are also broad peaks
associated with the G mode and D mode. These broad signals
do not change position but increase significantly in intensity
when the strain is increased beyond 0.5%. The broad
G-mode peaks have been noted previously and associated
with double-resonance features. The broad D-mode peak may
be associated with the introduction of defects in the nanotube
structure under high strain.
The results that we present here show quite significant
differences when compared with earlier measurements made
on nanotubes lying on a substrate20,21 and illustrate the
importance of systematic experimental studies of freely
suspended nanotubes accompanied by theoretical studies to
elucidate the complicated processes involved as nanotubes
are subjected to outside forces. Our measurement scheme
has considerable potential for the study of the intrinsic
structural and electronic properties of one-dimensionalnanostructures
under strain, such as SWNTs, double-walled CNT,
and other one-dimensional nanowires.
Acknowledgment. This work is supported by Vetenskapsrådet,
SSF, and STINT. One of the authors (S.W.L.)
is partially supported by the Korea Research Foundation
Grant funded by the Korean Government (MOEHRD) (KRF-
2005-214-C00198). The authors thank H. Brenning and B.
S. Kang for their help in preparing the Si cantilever structure
and with SEM observations.
Supporting Information Available: Full waterfall plots
for the Raman data obtained for SWNT2 and reversibilty
test results. This material is available free of charge via the
Internet at http://pubs.acs.org.results
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NL070877X
Nano Lett., Vol. 7, No. 9, 2007 2595
Suspended Individual Single-Walled
Carbon Nanotubes under Strain
Sang Wook Lee,† Goo-Hwan Jeong,† and Eleanor E. B. Campbell*,#
Department of Physics, Go¨teborg UniVersity, Go¨teborg, SE-412 96,Sweden
Received April 14, 2007; Revised Manuscript Received July 19,2007
ABSTRACT
We present a technique for in situ Raman measurements of suspendedindividual single-walled carbon nanotubes (SWNTs) under strain.We
observe a strong change in the radial breathing mode intensity withincreasing strain as the nanotube moves out of (or into) resonance,and
for strain greater than 2%, there is a clear irreversible upshiftin the G-mode frequencies accompanied by an increase in intensityof a broad
peak at a position associated with the D mode. For lower strain,the G-mode peaks (A1, E1, and E2) do not change significantly inposition but
change in relative intensity.
Due to their remarkable mechanical and electrical properties,
carbon nanotubes (CNT) continue to be the object of intense
experimental and theoretical investigation. Applications of
the CNT’s mechanical properties within lightweight composite
materials1 are now reaching commercial products, and
efforts are proceeding to increase the Young’s modulus of
nanotube yarns and mats to approach the theoretical limit.2
The mechanical and electrical properties of individual carbon
nanotubes have also been the object of much fundamental
interest. In recent years, CNT-based nanoelectromechanical
systems3-10 have been studied to investigate the interesting
coupling of electrical and mechanical behavior that occurs
on the nanoscale. The change of the electronic properties of
an individual CNT as mechanical force is applied is one of
the most intriguing issues within this larger topic.4-7
Structural and electronic properties of single-walled carbon
nanotubes (SWNTs) under strain have been theoretically
investigated by employing different calculation methods.11-13
Most of these theoretical studies deal with the changes of
bond lengths, radii, and band gaps of specific SWNTs as a
function of compressive and tensile strain. It is clear from
these results that the band gap of the SWNTs can change
significantly as strain is applied. This was confirmed in an
experimental study of transport measurements on individual
suspended SWNTs under strain.4 Concerning structural
changes, Pullen et al.13 recently used an ab initio approach
to show that there was a small, chirality-dependent, linear
increase in bond length with strain, except for bonds directed
along the nanotube circumference. They also predicted that
the radii remain unchanged under uniaxial strain up to 6%.
Resonant Raman spectroscopy is a powerful tool to probe
structural and electronic changes of SWNTs in experiment.14
There have been several experimental studies devoted to the
investigation of changes in the Raman spectra when applying
pressure or strain on bundles of SWNTs.15-19 The tangential
and radial breathing modes (RBM) of SWNT bundles were
shown to shift both under compressive15,16 and tensile17-19
force. In the case of SWNT bundles, there is the added
complication of the tube-tube interaction and how it affects
the Raman spectra under external forces. Cronin et al.20,21
reported Raman studies of individual SWNTs deposited on
a silicon substrate that were placed under strain bymanipulating
the nanotubes with an AFM tip (pushing the central
part of the nanotube across the substrate) and studying the
Raman spectra before and after manipulation. They observed
a very clear downshift in the position of the G band which
was much larger than that observed by the same group in
later experiments on bundles of nanotubes where the strain
was applied via an elastic polymer substrate.19 In all of the
studies reported so far, there have been interactions either
between individual nanotubes or between a nanotube and a
substrate, which can serve to complicate the effects. In the
present work, we apply strain to individual suspended
SWNTs grown between a Si cantilever and a support. The
strain is applied by deflecting the cantilever with an AFM
tip while simultaneously recording the Raman spectra. The
results are qualitatively different from those reported by
Cronin et al.20,21
The experiments were carried out using a combined
Renishaw/Nanonics micro-Raman/AFM setup. The AFM tip
* To whom correspondence should be addressed. E-mail:
Eleanor.Campbell@ed.ac.uk.
† Equal contribution to this work.
# Also at School of Chemistry, Edinburgh University, West MainsRoad,
Edinburgh EH9 3JJ, Scotland.
NANO
LETTERS
2007
Vol. 7, No. 9
2590-2595
10.1021/nl070877x CCC: $37.00 © 2007 American Chemical Society
Published on Web 08/25/2007
was used to deflect a Si cantilever which formed one support
of a suspended SWNT, shown in Figure 1. Axial strain was
applied to the nanotube by deflecting the cantilever via a
force applied by the AFM tip. As was the case for the studies
of nanotubes deposited on substrates, the deflection force
was applied perpendicular to the nanotube axis; however,
the resulting strain was primarily uniaxial.21 In the present
experiments, we could also rule out any contribution from
torsional strain, which was less straightforward for theearlier
studies. The micromechanical silicon cantilever structures
were fabricated by selective plasma etching of Si and wet
etching of SiO2 with buffered hydrofluoric acid. The dimensions
of the cantilever (70 ím long, 4 ím thick, 4 ím wide)
and the counterpart support platform were defined by electron
beam lithography on a silicon-on-insulator (SOI) wafer. The
distance between the cantilever and the platform was
typically 1-2 ím.
SWNTs were synthesized by thermal chemical vapor
deposition. As-purchased ferritin solution (Sigma Aldrich)
was diluted (0.01 vol %) with deionized water and deposited
on the cantilever to serve as the catalyst for SWNT growth.22
After calcination of the ferritin molecules, SWNTs were
grown using methane and hydrogen gas at 900 °C for 5 min.
The ferritin density was adjusted to ensure that, on average,
one suspended SWNT was grown between the cantilever and
the platform. Strain-force-dependent resonant Ramanspectroscopy
was performed on the individual suspended SWNTs
by combining an AFM head (Nanonics Imaging Ltd.) with
a micro-Raman measurement system (Renishaw) operated
with a 514.5 nm laser. The AFM tip was placed at the center
of the silicon cantilever. The cantilever was long enough to
avoid the screening of the laser beam by the AFM tip since
the average width of the commercially available AFM probe
is around 30 ím. The spring constant of the silicon cantilever
was estimated at the center by force-distance measurements
with an AFM tip (spring constant of the AFM cantilever
was 15 N/m) and found to be 18 N/m. From the force
calibration, shown in Figure 2, we could determine a linear
relationship between the deflection voltage of the AFM
system and the height difference at the center of the
cantilever. A deflection voltage of, for example, 0.5 V
induces a 22.5 nm height difference, corresponding to a
downward deflection of 45 nm at the end of the cantilever.
Resonant Raman spectroscopy measurements were done
while the AFM tip was pushing on the silicon cantilever.
Each time the force was increased on the cantilever, the laser
that monitored the deflection of the AFM tip was screened
by a homemade shutter to aid focusing and also to prevent
any interference with the Raman signal from the stretched
SWNT. It was also possible to check the position of the end
of the AFM tip when the shutter was in place, as shown in
the left-side inset of Figure 2. The focus of the micro-Raman
laser spot was adjusted to coincide with the suspended
SWNT after the spot was located exactly in the gap space
between the end of the silicon cantilever and the platform.
The focus was readjusted each time after increasing the
pushing force on the cantilever. As has been noted previously,
23 the Raman signal from suspended SWNTs is much
stronger than the signal from SWNTs lying on the substrate,
which, combined with the poor focus conditions in our
experiment for the nanotubes on the substrate, means that
we only detect the Raman signal from the suspended
nanotube.
Figure 3a shows the strain-force dependence of the
resonant Raman spectra of a suspended SWNT. The maximum
strain used in this series of measurements was estimated
to be 1%. There is some uncertainty in this value due to
the uncertainty in the amount of slack present initially in
the suspended nanotube and the possible influence of
slippage at the high deflections. The strain values used
throughout this paper are estimated assuming an initially taut
nanotube and no slippage. We have carried out systematic
measurements to estimate the effect of slippage. We did not
observe any indication of slippage for nominal applied strain
of up to 1%. We have also not observed any abrupt changes
in the Raman spectrum for these relatively low strain values
that can be attributed to slippage, as was observed by Kumar
and Cronin for nanotube bundles.19 Beyond this nominal
strain value, we observed irreversible changes in the Raman
spectra due to damage of the nanotubes. It is probable that
a certain degree of slippage was occurring for these extreme
strain values, but at present, this is difficult to quantify.
The frequencies and fwhm of the measured Raman peaks
were determined by fitting the spectra assuming Lorentzian
line shapes. The error bar on the experimental frequency and
Figure 1. (a) Typical SEM image of silicon cantileverstructure.
Scale bar shows 10 ím. Inset: zoomed-in SEM image of individual
SWNTs suspended between the end of the cantilever and the
platform. (b) Schematic configuration of the setup for astrain-forcedependent
in situ resonant Raman measurement. L0 is the length
of the suspended SWNT, and 2ä is the downward distance of the
SWNT due to deflection of the silicon cantilever by AFM tip
manipulation.
Nano Lett., Vol. 7, No. 9, 2007 2591
fwhm is typically on the order of 1 cm-1. The radial breathing
mode is clearly seen at 169 cm-1. According to the
relationship given by Meyer et al.,24 determined forfreestanding
SWNTs, this corresponds to a semiconducting
nanotube with a diameter of 1.45 nm and is most probably
an (11,10) nanotube. Examples of some fitted tangential (Gband)
modes for the same nanotube are shown in Figure 3b.
The Raman laser was not aligned parallel to the nanotube
axis so all six allowed transitions could be observed,
corresponding to transitions with A, E1, and E2 symmetry
for both the G+ and G- bands. The peak positions and fwhm,
determined without strain applied to the nanotube, are listed
in Table 1 (SWNT1). There is an upshift/downshift (öG-
/öG+) in the measured frequencies compared to the values
reported for nanotubes of the same diameter isolated on a
Si/SiO2 substrate25 by 3-5 cm-1 for the A and E1 transitions
and by +12 cm-1 (öG-) and -16 cm-1 (öG+) for the E2
transitions. A similar trend is noted for the second nanotube
(öRBM ) 186 cm-1, d ) 1.28 nm, most probably (10,9)),
whose values are given in Table 1 (SWNT2, spectra provided
as Supporting Information). All six Lorentzians are needed
to obtain a good fit to the data, although the E2 transitions
are typically lower in intensity than the A and E1 transitions.
The fitted line widths are consistent with the natural line
widths of the transitions.26 In addition to the sharp peaks, it
is also necessary (in particular for high strain) to fit broad
features at 1540 (fwhm ca. 100 cm-1) and 1610 cm-1
(fwhm ca. 60 cm-1). These features have been noted
previously in weakly resonant G-band spectra fromsemiconducting
SWNTs and associated with a double-resonance
process.14,25,27 We observe that the broad features are more
intense in spectra with small radial breathing modeintensities,
that is, for tubes that are only weakly resonant, in
agreement with previous observations.
Some clear tendencies can be observed in the straindependent
measurements. The radial breathing mode frequency
does not shift with increasing strain within our
experimental uncertainty. This is in agreement with recent
calculations13 and with the experimental study of individual
strained nanotubes on a substrate by Cronin et al.20 However,
in contrast to the study of Cronin et al., we do observe a
clear change in the intensity of the radial breathing mode
transition. This is shown in more detail in Figure 4 where
the integrated RBM peak intensities are plotted as a function
of the AFM deflection voltage (and estimated strain). Two
sets of data are shown here. Figure 4a corresponds to the
spectra shown in Figure 3 and Figure 4b to the results from
SWNT2. The strain applied to the nanotube can be estimated
according to the approximate relation strain [%] ) B voltage2, withB ) 0.1 for SWNT1 (length ) 2 ím) and B
) 0.4 for SWNT2 (length ) 1 ím). For SWNT1, which
initially showed an intense RBM signal, the intensity falls
off linearly with increasing strain until it disappearscompletely
for AFM deflection voltages greater than 2.5 V
(estimated strain > 0.6%). For SWNT2, which initially
showed a very weak RBM peak (indicating only weak
resonance), the RBM intensity first increases as strain is
applied, reaching a maximum for a strain of approximately
0.4%, and then decreases toward zero. This can be explained
in terms of the deformation of the electronic band structure
with the application of strain.13,17 The experimental resonance
window for the RBM of isolated, suspended nanotubes is
on the order of 8 meV.28 Band gap changes significantly
larger than this can be expected for the strains applied in
the present experiments.4,13 The overall intensity of the G
band does not change so dramatically (the resonance window
is much less critical for the G peaks since the phonon energy
is larger28), but a close look at the spectra in Figure 3 shows
Figure 2. Force-deflection curve of a silicon cantilever. Thepushing force is applied in the middle of the cantilever using AFMtip
manipulation. Upper inset: optical microscope image of the devicewhen the AFM tip pushed the cantilever (upper) before and(lower)
after the shutter screened the laser from the AFM head. Lowerinset: force-displacement curve measured on the cantilever (redline) and
on a Si substrate (black line) for calibration of the springconstant of the cantilever.
2592 Nano Lett., Vol. 7, No. 9, 2007
that the relative intensities of the A and E1 peaks of the G+
band undergo strong changes as strain is applied. This
behavior has been found to be strongly dependent on the
individual nanotube, with some nanotubes showing relatively
little change in relative intensities for a similar nominalstrain
range. However, the changes in the relative intensities for a
given individual nanotube are reproducible and reversible.
Figure 5 shows that the G+ A/E1 ratio for SWNT1 reaches
a minimum for AFM deflection voltages in the range of 0.4-
1.5 V (ca. 0.16-0.22% strain) before rapidly increasing again
to a maximum at 2.5 V (0.6% strain). Interestingly, the
minimum in the G+ A/E1 ratio is accompanied by the
appearance of a small, narrow peak at the position of the D
mode (1333 cm-1, fwhm 5 cm-1). Such behavior is not
observed for every nanotube, and we assume that it is related
to a resonant process with a relatively narrow resonance
window. Detailed ab initio calculations are required to
elucidate the mechanisms for these changes, but it is clear
from these spectra that strain measurements on suspended
nanotubes have the potential to provide a very stringent test
of theoretical studies of the electronic structure andtransition
matrix elements of individual nanotubes.
The G-band peak positions are plotted in Figure 6 as a
function of the applied strain for SWNT1 (Figure 5a) and
SWNT2 (Figure 5b). In contrast to the study of Cronin et
al. for nanotubes deposited on a substrate,20,21 we do not
observe any down-shift in the frequencies of the G-band
transitions. For both nanotubes, we observe an increase in
the frequencies as the strain is increased beyond a certain
critical value (ca. 2% in both cases). This effect is more
apparent for SWNT2 (Figure 5b), which is exposed to higher
strain and where it is also possible to see that the frequency
shift is larger for the G- peaks than that for the G+ peaks.
Figure 3. Deflection-force-dependent in situ resonance Raman
spectroscopy result on a suspended individual SWNT. (a) Change
of Raman spectra depending on AFM deflection voltage (lower
x-axis) and estimated strain (upper x-axis) from 0.0 to 3.0 V.(b)
G-band peak fits for three different values of the estimatedstrain.
Table 1. Fitted Lorentzian Peak Positions and fwhm for TwoSuspended SWNTs without the Application of Strain; the DiameterHas
Been Calculated Using the Expression Given by Meyer et al.,24 öRBM[cm-1] ) 204/d [nm] + 27
RBM diam. G-A G- E1 G- E2 G+A G+ E1 G+ E2
SWNT1, ö 169 1.45 nm 1572 1576 1566 1590 1586 1594
SWNT1, fwhm 5 5 4 5 6 5.3 6
SWNT2, ö 186 1.28 nm 1568 1575 1563 1590.5 1586 1595
SWNT2, fwhm 7 7 7 7 6 5.3 6
Figure 4. Integrated radial breathing mode (RBM) intensity as a
function of AFM deflection voltage (lower x axis) and estimated
strain (upper x axis) for (a) SWNT1 and (b) SWNT2.
Nano Lett., Vol. 7, No. 9, 2007 2593
For an applied AFM deflection voltage of 5 V or higher on
SWNT2 (g10% strain), it was not possible to resolve the
individual peaks and, only two Lorentzians were used to fit
the data instead of six. Once we observed this shift in the
G-peak frequencies, the spectral changes were no longer
reversible. We therefore attribute the change in thefrequencies
to the occurrence of damage in the nanotubes.
In addition to the small, sharp D peak visible in the spectra
shown in Figure 3a, there is a much broader peak centered
at 1367 cm-1 (independent of applied strain) with a fwhm
of 200 cm-1. This becomes clearly visible for large strain
and is observed in both sets of spectra (SWNT1 and
SWNT2). The integrated peak intensities for both nanotubes
are plotted in Figure 6c as a function of AFM deflection
voltage. We often observe a small, finite, broad peak intensity
for zero force applied to the silicon cantilever, which then
disappears for low values of strain (up to ca. 1%) before
increasing strongly as the strain is increased beyond this
value. Such behavior can be clearly seen in Figure 6c for
both samples. The finite peak intensity for zero force may
be related to initial slack in the suspended nanotube, although
this is too small to be observed by SEM. Alternatively, it is
conceivable that the application of a small strain can help
heal some intrinsic defects in the nanotube.
In summary, we have measured in situ Raman spectroscopy
of suspended individual SWNTs under strain. The
position of the radial breathing mode frequency remains
constant as strain is increased, but the intensity changes due
to the modification of the band structure, leading to a change
in the resonance conditions. This observation is in agreement
with calculations for semiconducting nanotubes.13,17,21 The
results concerning the G-mode peaks are more unexpected.
One would intuitively expect that an increase in nanotube
length would lead to a corresponding increase in the bond
length in the axial direction and hence to an expected
decrease in frequency. A large down-shift was also observed
in earlier experimental work.20,21 However, in the present
experiments, the positions of the G-mode peaks do not
change significantly until the strain exceeds 2%, when one
can observe an upshift in the frequency. These changes to
the spectra are irreversible and indicate that structuralchanges
have occurred. The effect is most pronounced for the Gpeaks.
Below this, although the peak positions remain
constant, there can be strong variations in the relative peak
intensities both for the G mode and the D mode. These
changes are reversible and are attributed to changes in the
band structure affecting the resonance conditions. Both
Figure 5. (a) Ratio of integrated A/E1 peak intensities(triangles
and left-hand y axis) and (b) the integrated sharp (1333 cm-1,fwhm
5 cm-1) D-peak intensity (stars, right-hand axis) as a functionof
AFM deflection voltage (lower x axis) and estimated strain(upper
x axis). The integrated peak intensities were normalized to theSi
peak intensity for each spectrum.
Figure 6. (a) G-mode peak positions as a function of AFM
deflection voltage (lower x axis) and strain (upper x axis) for
SWNT1. (b) G-mode peak positions as a function of AFM
deflection voltage (lower x axis) and strain (upper x axis) for
SWNT2. The large error bars for 5 and 5.5 V indicate that the
individual peaks could not be clearly resolved, and both the G+
and G- bands were each fitted with a single Lorentzian. Thedotted
lines mark the initial position of the peak for zero appliedstrain
and are simply to aid the eye. (c) Integrated broad D-modeintensity
(1367 cm-1, fwhm 200 cm-1) as a function of estimated strainfor
SWNT1 (squares) and SWNT2 (stars).
2594 Nano Lett., Vol. 7, No. 9, 2007
nanotubes that we studied in detail in the present paper are
very close to the armchair in geometries (11,10) and (10,9).
We would therefore not expect a significant shift in the
frequencies of the transverse G- peaks, in agreement with
our experimental observations, since the relevant bond
lengths would not be significantly effected by the appliance
of axial strain. However, we would still expect thelongitudinal
G+ peaks to shift downward. Reich et al.29 carried out
full ab initio calculations on two chiral nanotubes and showed
that chiral tubes yield qualitatively and quantitativelydifferent
results from achiral ones, with evidence for a strong
mixing of the optical modes. The situation is therefore
considerably more complex than might be assumed from
tight-binding calculations, and we hope that our present
results might stimulate more theoretical studies into the
properties of chiral nanotubes.
In addition to the sharp Lorentzian peaks that have a fwhm
close to the natural line width, there are also broad peaks
associated with the G mode and D mode. These broad signals
do not change position but increase significantly in intensity
when the strain is increased beyond 0.5%. The broad
G-mode peaks have been noted previously and associated
with double-resonance features. The broad D-mode peak may
be associated with the introduction of defects in the nanotube
structure under high strain.
The results that we present here show quite significant
differences when compared with earlier measurements made
on nanotubes lying on a substrate20,21 and illustrate the
importance of systematic experimental studies of freely
suspended nanotubes accompanied by theoretical studies to
elucidate the complicated processes involved as nanotubes
are subjected to outside forces. Our measurement scheme
has considerable potential for the study of the intrinsic
structural and electronic properties of one-dimensionalnanostructures
under strain, such as SWNTs, double-walled CNT,
and other one-dimensional nanowires.
Acknowledgment. This work is supported by Vetenskapsrådet,
SSF, and STINT. One of the authors (S.W.L.)
is partially supported by the Korea Research Foundation
Grant funded by the Korean Government (MOEHRD) (KRF-
2005-214-C00198). The authors thank H. Brenning and B.
S. Kang for their help in preparing the Si cantilever structure
and with SEM observations.
Supporting Information Available: Full waterfall plots
for the Raman data obtained for SWNT2 and reversibilty
test results. This material is available free of charge via the
Internet at http://pubs.acs.org.results
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